The proof, in Appendix REF , is similar to the proof of Theorem REF . Using again the general bound of the regret of OMD algorithms in Bubeck [1]}, we bound the diameter of \(\mathcal {X}\)  w.r.t. to the Bregman divergence as well as the dual norm \(\left\Vert \cdot \right\Vert _\infty \)  of gradients \(\nabla f_{\mathbf {r}_t}(\mathbf {x}_t)\) .
